Construction of compact embedded $\lambda$-hypersurfaces via isoparametric hypersurfaces

Abstract

We construct closed embedded $\lambda$-hypersurfaces in ${\mathbb{R}}^{n+1}$ of topological type $S^1\times M$ for any $\lambda \ge 0$, where $M\subset {\mathbb{S}}^n$ is an isoparametric hypersurface with equal principal curvature multiplicities. This extends previous results of Angenent, McGrath, and Riedler (for $\lambda =0$) as well as Cheng-Wei and Ross (for $\lambda >0$), and in particular completes the missing case of Riedler's construction.

arXiv comment17 pages, Comments Welcome!